I don’t think cycles is working
Welcome to Blender!  It's a big, complicated piece of software where lots of things can go wrong, and it takes a lot of practice to get used to it, so no real surprise that you had a tough night working on this.

In the posted .blend file, the "inner crystal" had no material, so maybe you uploaded it before shading it green and blue.

The "outer clear part of crystal" did have a reasonable glass material.  It looked like this in my Cycles preview, with a fuzzy version of the inner crystal just visible.  Did it look anything like this for you?



If so, the main problem with the "outer clear part of crystal" material is probably the high roughness which makes it look pretty opaque.  If I turn the roughness value down to 0.25 in the principled shader, add a blue emission shader material to the "inner crystal", kick the area light strength up from 1 to 50 (i.e. 5000 Watts), and add a couple duplicate area lights, also 5000 Watts, it starts to look better.



Here's a .blend file with the changes I made.  If you load this up, switch to the "Rendered" view, and don't see a blue crystal like the image above, then yes, something's wrong with Cycles running on your admittedly underpowered computer.



Note that it looks even better if I select both the inner and outer crystal and stretch them out on the Z-axis ("s" to size, "z" to size along Z-axis, and move the mouse to stretch it vertically before left clicking).  The longer crystal reflects light better.

Getting this scene working with Eevee would be tough.  Eevee doesn't do a great job with accurate handling of area lights and glass materials.  But, you could try the following:


In the Render Properties panel, switch your Render Engine from Cycles to Eevee.  Further down in the panel, click on the "Screen Space Reflections" checkbox, open that subpanel, and check the "Refraction" checkbox.
Click on your "outer clear part of crystal", go to its Material Properties panel, and scroll down to the "Settings" subpanel.  In that subpanel, change "Blend Mode" from "Opaque" to "Alpha Blend", and below that turn on the "Screen Space Refraction" checkbox.


Switch to the Render view, and you should have something like this:



It looks pretty ugly and underwhelming, though it does look kind of cool if you middle-mouse-button drag the view around.

Anyway, hope that helps.